Theory of subgap interchain tunneling in quasi one-dimensional conductors

TL;DR

This paper develops a theoretical framework for understanding subgap interchain tunneling in quasi-one-dimensional conductors with charge density waves, revealing power-law threshold behaviors and the effects of dimensionality and temperature.

Contribution

It introduces an instanton-based theory for coherent tunneling in the pseudogap region, accounting for both single-electron and bi-electron channels in quasi-1D systems.

Findings

Single-electron tunneling occurs below the gap down to the pair-breaking threshold.

Bi-electronic tunneling extends down to zero bias in the 1D regime.

Threshold behaviors follow power laws with exponents related to Fermi and phase velocities.

Abstract

We suggest a theory of internal coherent tunneling in the pseudogap region, when the applied voltage U is below the free electron gap 2Delta_0. We address quasi 1D systems, where the gap is originated by spontaneous lattice distortions of the Incommensurate Charge Density Wave (ICDW) type. Results can be adjusted also to quasi-1D superconductors. The instanton approach allows to calculate the interchain tunneling current both in single electron (amplitude solitons, i.e. spinons) and bi-electron (phase slips) channels. Transition rates are governed by a dissipative dynamics originated by emission of gapless phase excitations in the course of the instanton process. We find that the single-electron tunneling is allowed below the nominal gap 2Delta_0 down to the true pair-breaking threshold at 2W_as<2Delta, where W_as=2Delta/pi is the amplitude soliton energy. Most importantly, the bi-electronic tunneling stretches down to U=0 (in the 1D regime). In both cases, the threshold behavior is given by power laws J (U-U_c)^beta, where the exponent beta v_F/u is large as the ratio of the Fermi velocity v_F and the phase one u. In the 2D or 3D ordered phases, at temperature T<T_c, the one-electron tunneling current does not vanish at the threshold U_c anymore, but saturates above it at U-U_c T_c<<Delta. Also the bi-particle channel acquires a finite threshold U_c=W_ph T_c<<Delta at the energy W_ph of the 2\pi phase soliton.